
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import entropy, norm
from statsmodels.stats.outliers_influence import variance_inflation_factor
from statsmodels.tools.tools import add_constant
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression, LogisticRegression
from sklearn.decomposition import PCA
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from scipy.stats import chi2
pd.set_option('display.max_columns', None)

mimic = pd.read_csv("health_dataset.csv")
data = mimic.copy()
display(data.head())
print(f"This dataset contains {data.shape[0]} rows and {data.shape[1]} columns.")

This dataset contains 22565 rows and 30 columns.


# Split the dataset
data0 = data[data['HOSPITAL_EXPIRE_FLAG'] == 0]
data1 = data[data['HOSPITAL_EXPIRE_FLAG'] == 1]

# Display the first few rows of each DataFrame to verify
print("Data0 (HOSPITAL_EXPIRE_FLAG == 0):")
display(data0.head())

print("Data1 (HOSPITAL_EXPIRE_FLAG == 1):")
display(data1.head())

# Print the shapes to confirm the number of rows in each DataFrame
print(f"Data0 contains {data0.shape[0]} rows and {data0.shape[1]} columns.")
print(f"Data1 contains {data1.shape[0]} rows and {data1.shape[1]} columns.")

Data0 (HOSPITAL_EXPIRE_FLAG == 0):

Data1 (HOSPITAL_EXPIRE_FLAG == 1):

Data0 contains 19286 rows and 30 columns.
Data1 contains 3279 rows and 30 columns.


def Missing_Values(data):
    var_name = []
    data_type = []
    total_value = []
    total_missing_value = []
    missing_value_pct = []
    unique_value = []
    total_unique_value = []

    
    for col in data.columns:
        var_name.append(col)
        data_type.append(data[col].dtype)
        total_value.append(data[col].shape[0])
        total_missing_value.append(data[col].isnull().sum())
        missing_value_pct.append(round(data[col].isnull().sum()/data[col].shape[0],3))
        unique_value.append(data[col].unique())
        total_unique_value.append(len(data[col].unique()))
        
    missing_data=pd.DataFrame({"Variable":var_name,\
                               "Data_Type":data_type,\
                               "No_Total_Value":total_value,\
                               "No_Total_Missing_Value":total_missing_value,\
                               "Proportion_Missing_Value":missing_value_pct,\
                               "Unique_Value":unique_value,\
                               "Total_Unique_Value":total_unique_value
                              })
    
    missing_data = missing_data.set_index("Variable")
    return missing_data


# Checking missing values for the entire dataset
Missing_Values(data)


# Checking missing values for patients who expired
Missing_Values(data0)


# Checking missing values for patients who survived
Missing_Values(data1)


# Drop specified columns from the data DataFrame
data = data.drop(columns=['SUBJECT_ID', 'HADM_ID', 'ICUSTAY_ID'])

# Display the first few rows of the modified data DataFrame
display(data.head())

# Print the shape of the modified data DataFrame
print(f"This dataset contains {data.shape[0]} rows and {data.shape[1]} columns.")

This dataset contains 22565 rows and 27 columns.


target = ['HOSPITAL_EXPIRE_FLAG']

target_counts = data[target[0]].value_counts()
plt.figure(figsize=(8, 8))
plt.pie(target_counts, labels=target_counts.index, autopct='%1.1f%%', colors=['#66b3ff','#ff9999'], startangle=140)
plt.title(f'Pie Chart for {target[0]} (Percentage)')
plt.axis('equal')  # Equal aspect ratio ensures that pie is drawn as a circle.
plt.show()


cat_cols = ['GENDER', 'ETHNICITY']
            
# Create bar charts with percentages
for col in cat_cols:
    plt.figure(figsize=(6, 8))
    ax = sns.countplot(data=data, x=col, palette='viridis')
    total = len(data[col])
    for p in ax.patches:
        frequency = p.get_height()
        percentage = f'{100 * frequency / total:.1f}%'
        x = p.get_x() + p.get_width() / 2 - 0.1
        y = p.get_height() + 0.005 * total
        ax.annotate(f'{percentage}', (x, y), size=10, ha='center')
    plt.title(f'Bar Chart for {col}')
    plt.xlabel(col)
    plt.ylabel('Count')
    plt.xticks(rotation=90)
    plt.show()


num_cols_information = [
    {"Feature": "AGE", "Description": "The age of the patient.", "MIN": 0, "MAX": 91, "UNIT": "years"},
    {"Feature": "HEART_RATE", "Description": "Heart Rate: The average heart rate of the patient.", "MIN": 0, "MAX": 350, "UNIT": "bpm"},
    {"Feature": "DIASBP", "Description": "Diastolic Blood Pressure (diasbp): The average diastolic blood pressure of the patient.", "MIN": 0, "MAX": 375, "UNIT": "mmHg"},
    {"Feature": "SYSTBP", "Description": "Systolic Blood Pressure (systbp): The average systolic blood pressure of the patient.", "MIN": 0, "MAX": 375, "UNIT": "mmHg"},
    {"Feature": "MABP", "Description": "Mean Blood Pressure (meanbp): The average mean blood pressure of the patient.", "MIN": 14, "MAX": 330, "UNIT": "mmHg"},
    {"Feature": "TEMPERATURE", "Description": "Temperature: The average body temperature of the patient.", "MIN": 78.8, "MAX": 113, "UNIT": "°F"},
    {"Feature": "O2SAT", "Description": "Oxygen Saturation (o2sat): The average oxygen saturation of the patient.", "MIN": 0, "MAX": 100, "UNIT": "%"},
    {"Feature": "RESP_RATE", "Description": "Respiratory Rate (resp_rate): The average respiratory rate of the patient.", "MIN": 0, "MAX": 300, "UNIT": "breaths per minute"},
    {"Feature": "ALBUMIN", "Description": "Albumin: The average albumin level in the blood.", "MIN": 0.6, "MAX": 6, "UNIT": "g/dL"},
    {"Feature": "BUN", "Description": "Blood Urea Nitrogen (bun): The average blood urea nitrogen level.", "MIN": 0, "MAX": 250, "UNIT": "mg/dL"},
    {"Feature": "BILIRUBIN", "Description": "Bilirubin: The average bilirubin level.", "MIN": 0.1, "MAX": 60, "UNIT": "mg/dL"},
    {"Feature": "LACTATE", "Description": "Lactate: The average lactate level in the blood.", "MIN": 0.4, "MAX": 30, "UNIT": "mmol/L"},
    {"Feature": "BICARBONATE", "Description": "Bicarbonate: The average bicarbonate level.", "MIN": 0, "MAX": 60, "UNIT": "mEq/L"},
    {"Feature": "CHLORIDE", "Description": "Chloride: The average chloride level.", "MIN": 50, "MAX": 175, "UNIT": "mEq/L"},
    {"Feature": "CREATININE", "Description": "Creatinine: The average creatinine level.", "MIN": 0.1, "MAX": 60, "UNIT": "mg/dL"},
    {"Feature": "GLUCOSE", "Description": "Glucose: The average glucose level.", "MIN": 33, "MAX": 2000, "UNIT": "mg/dL"},
    {"Feature": "HEMOGLOBIN", "Description": "Hemoglobin: The average hemoglobin level.", "MIN": 0, "MAX": 25, "UNIT": "g/dL"},
    {"Feature": "HEMATOCRIT", "Description": "Hematocrit: The average hematocrit level.", "MIN": 0, "MAX": 75, "UNIT": "g/dL"},
    {"Feature": "PLATELET_COUNT", "Description": "Platelet Count: The average platelet count.", "MIN": 0, "MAX": 2000, "UNIT": "1000/mm³"},
    {"Feature": "POTASSIUM", "Description": "Potassium: The average potassium level.", "MIN": 0, "MAX": 12, "UNIT": "mEq/L"},
    {"Feature": "PTT", "Description": "Partial Thromboplastin Time (PTT): The average partial thromboplastin time.", "MIN": 18.8, "MAX": 150, "UNIT": "seconds"},
    {"Feature": "SODIUM", "Description": "Sodium: The average sodium level.", "MIN": 50, "MAX": 225, "UNIT": "mEq/L"},
    {"Feature": "WBC", "Description": "White Blood Cells: The average white blood cell count.", "MIN": 0, "MAX": 1000, "UNIT": "1000/mm³"},
    {"Feature": "BAND_NEUTROPHIL", "Description": "Band Neutrophil: The percentage of band neutrophils.", "MIN": 0, "MAX": 100, "UNIT": "%"}
]
pd.DataFrame(num_cols_information)


num_cols = ['AGE', 'HEART_RATE', 'DIASBP', 'SYSTBP', 'MABP', 'TEMPERATURE', 'O2SAT', 'RESP_RATE', 'ALBUMIN', 'BUN', 'BILIRUBIN', 'LACTATE', 'BICARBONATE', 'CHLORIDE', 'CREATININE', 'GLUCOSE', 'HEMOGLOBIN', 'HEMATOCRIT', 'PLATELET_COUNT', 'POTASSIUM', 'PTT', 'SODIUM', 'WBC', 'BAND_NEUTROPHIL']


# For the entire observations

results = []
for col_info in num_cols_information:
    feature = col_info["Feature"]
    min_val = col_info["MIN"]
    max_val = col_info["MAX"]
    
    missing_count = data[feature].isnull().sum()
    below_min_count = (data[feature] < min_val).sum()
    above_max_count = (data[feature] > max_val).sum()
    
    results.append({
        "Feature": feature,
        "Missing Values": missing_count,
        "Below MIN": below_min_count,
        "Above MAX": above_max_count
    })

# Convert results to DataFrame
results_df = pd.DataFrame(results)

results_df["Total Valid Values"] = data.shape[0] - results_df["Missing Values"] - results_df["Below MIN"] - results_df["Above MAX"]

results_df


# For patients who expired

results = []
for col_info in num_cols_information:
    feature = col_info["Feature"]
    min_val = col_info["MIN"]
    max_val = col_info["MAX"]
    
    missing_count = data0[feature].isnull().sum()
    below_min_count = (data0[feature] < min_val).sum()
    above_max_count = (data0[feature] > max_val).sum()
    
    results.append({
        "Feature": feature,
        "Missing Values": missing_count,
        "Below MIN": below_min_count,
        "Above MAX": above_max_count
    })

# Convert results to DataFrame
results_df = pd.DataFrame(results)

results_df["Total Valid Values"] = data0.shape[0] - results_df["Missing Values"] - results_df["Below MIN"] - results_df["Above MAX"]

results_df


# For patients who did not expire

results = []
for col_info in num_cols_information:
    feature = col_info["Feature"]
    min_val = col_info["MIN"]
    max_val = col_info["MAX"]
    
    missing_count = data1[feature].isnull().sum()
    below_min_count = (data1[feature] < min_val).sum()
    above_max_count = (data1[feature] > max_val).sum()
    
    results.append({
        "Feature": feature,
        "Missing Values": missing_count,
        "Below MIN": below_min_count,
        "Above MAX": above_max_count
    })

# Convert results to DataFrame
results_df = pd.DataFrame(results)

results_df["Total Valid Values"] = data1.shape[0] - results_df["Missing Values"] - results_df["Below MIN"] - results_df["Above MAX"]

results_df


# Process each column
for col_info in num_cols_information:
    feature = col_info["Feature"]
    min_val = col_info["MIN"]
    max_val = col_info["MAX"]
    
    # Replace values below min_val with min_val and values above max_val with max_val
    data[feature] = np.where(data[feature] < min_val, np.nan, data[feature])
    data[feature] = np.where(data[feature] > max_val, np.nan, data[feature])
    
    # Calculate statistics
    missing_count = data[feature].isnull().sum()
    below_min_count = (data[feature] < min_val).sum()
    above_max_count = (data[feature] > max_val).sum()
    
    results.append({
        "Feature": feature,
        "Missing Values": missing_count,
        "Below MIN": below_min_count,
        "Above MAX": above_max_count
    })


results = []
for col_info in num_cols_information:
    feature = col_info["Feature"]
    min_val = col_info["MIN"]
    max_val = col_info["MAX"]
    
    missing_count = data[feature].isnull().sum()
    below_min_count = (data[feature] < min_val).sum()
    above_max_count = (data[feature] > max_val).sum()
    
    results.append({
        "Feature": feature,
        "Missing Values": missing_count,
        "Below MIN": below_min_count,
        "Above MAX": above_max_count
    })

# Convert results to DataFrame
results_df = pd.DataFrame(results)

results_df["Total Valid Values"] = data.shape[0] - results_df["Missing Values"] - results_df["Below MIN"] - results_df["Above MAX"]

results_df


# Store the results
kl_divergence_results = []

# Function to calculate KL divergence
def kl_divergence(p, q):
    return entropy(p, q)

# Iterate over each numerical column
for col in num_cols:
    col_data = data[col]
    
    # Calculate the probability distributions
    hist, bin_edges = np.histogram(col_data.dropna(), bins=30, density=True)
    
    # Assume normal distribution as reference distribution
    reference_distribution = norm.pdf(bin_edges[:-1], np.mean(col_data.dropna()), np.std(col_data.dropna()))
    
    # Normalize the histogram to make it a valid probability distribution
    hist /= np.sum(hist)
    reference_distribution /= np.sum(reference_distribution)
    
    # Calculate KL divergence
    kl_div = kl_divergence(hist, reference_distribution)
    kl_divergence_results.append({'Feature': col, 'KL Divergence': kl_div})

# Convert results to DataFrame
kl_divergence_df = pd.DataFrame(kl_divergence_results)

# Display KL divergence results
print(kl_divergence_df)

            Feature  KL Divergence
0               AGE       0.065410
1        HEART_RATE       0.040932
2            DIASBP       0.050021
3            SYSTBP       0.031161
4              MABP       0.233120
5       TEMPERATURE       0.293524
6             O2SAT       0.332655
7         RESP_RATE       0.256400
8           ALBUMIN       0.025676
9               BUN       0.300652
10        BILIRUBIN       1.247126
11          LACTATE       0.396055
12      BICARBONATE       0.053181
13         CHLORIDE       0.035973
14       CREATININE       0.531383
15          GLUCOSE       0.225293
16       HEMOGLOBIN       0.073793
17       HEMATOCRIT       0.080001
18   PLATELET_COUNT       0.156950
19        POTASSIUM       0.060117
20              PTT       0.355429
21           SODIUM       0.048403
22              WBC       0.471390
23  BAND_NEUTROPHIL       0.586817


# Define the number of columns for the plot
num_columns = 3

# Calculate the number of rows needed
num_rows = int(np.ceil(len(num_cols) / num_columns))

# Create a figure and a set of subplots
fig, axs = plt.subplots(num_rows, num_columns, figsize=(15, num_rows * 5))

# Flatten the axes array for easier indexing
axs = axs.flatten()

# Iterate over each numerical column to plot histograms
for idx, col in enumerate(num_cols):
    col_data = data[col]
    
    # Plot histogram
    sns.histplot(col_data, kde=True, bins=30, ax=axs[idx])
    axs[idx].set_title(f'Histogram of {col}')
    axs[idx].set_xlabel(col)
    axs[idx].set_ylabel('Frequency')

# Remove any empty subplots
for idx in range(len(num_cols), len(axs)):
    fig.delaxes(axs[idx])

plt.tight_layout()
plt.show()


missing_values_heart_rate0 = data0['HEART_RATE'].isnull().sum()
print(f"Number of missing values in HEART_RATE for Class 0: {missing_values_heart_rate0}")
missing_values_heart_rate1 = data1['HEART_RATE'].isnull().sum()
print(f"Number of missing values in HEART_RATE for Class 1: {missing_values_heart_rate1}")

Number of missing values in HEART_RATE for Class 0: 1
Number of missing values in HEART_RATE for Class 1: 0


# Calculate the mean of HEART_RATE from data0
mean_heart_rate = data0['HEART_RATE'].mean()
print(f"Mean HEART_RATE from data0: {mean_heart_rate}")

# Replace missing values in HEART_RATE of data with the mean from data0
data['HEART_RATE'].fillna(mean_heart_rate, inplace=True)

# Verify the replacement
missing_values_heart_rate_after = data['HEART_RATE'].isnull().sum()
print(f"Number of missing values in HEART_RATE after replacement: {missing_values_heart_rate_after}")

Mean HEART_RATE from data0: 83.74654869370609
Number of missing values in HEART_RATE after replacement: 0


missing_values_DIASBP0 = data0['DIASBP'].isnull().sum()
print(f"Number of missing values in DIASBP for Class 0: {missing_values_DIASBP0}")
missing_values_DIASBP1 = data1['DIASBP'].isnull().sum()
print(f"Number of missing values in DIASBP for Class 1: {missing_values_DIASBP1}")

Number of missing values in DIASBP for Class 0: 8997
Number of missing values in DIASBP for Class 1: 1268


missing_values_SYSTBP0 = data0['SYSTBP'].isnull().sum()
print(f"Number of missing values in SYSTBP for Class 0: {missing_values_SYSTBP0}")
missing_values_SYSTBP1 = data1['SYSTBP'].isnull().sum()
print(f"Number of missing values in SYSTBP for Class 1: {missing_values_SYSTBP1}")

Number of missing values in SYSTBP for Class 0: 9003
Number of missing values in SYSTBP for Class 1: 1269


data = data.drop(columns=['DIASBP', 'SYSTBP'])


data = data.drop(columns=['MABP', 'O2SAT'])


data = data.drop(columns=['BAND_NEUTROPHIL'])


# Calculate the median of TEMPERATURE from data0
median_temperature = data0['TEMPERATURE'].median()
print(f"Median TEMPERATURE from data0: {median_temperature}")

# Replace missing TEMPERATURE values in data where HOSPITAL_EXPIRE_FLAG is 0
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['TEMPERATURE'].isnull())
data.loc[condition, 'TEMPERATURE'] = median_temperature

# Calculate the median of TEMPERATURE from data1
median_temperature = data1['TEMPERATURE'].median()
print(f"Median TEMPERATURE from data1: {median_temperature}")

# Replace missing TEMPERATURE values in data where HOSPITAL_EXPIRE_FLAG is 1
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 1) & (data['TEMPERATURE'].isnull())
data.loc[condition, 'TEMPERATURE'] = median_temperature

Median TEMPERATURE from data0: 98.3
Median TEMPERATURE from data1: 98.2625


median_RESP_RATE = data0['RESP_RATE'].median()
print(f"Median RESP_RATE from data0: {median_RESP_RATE}")

condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['RESP_RATE'].isnull())
data.loc[condition, 'RESP_RATE'] = median_RESP_RATE

Median RESP_RATE from data0: 19.625


# Calculate the median of ALBUMIN from data0
median_albumin = data0['ALBUMIN'].median()
print(f"Median ALBUMIN from data0: {median_albumin}")

# Replace missing ALBUMIN values in data where HOSPITAL_EXPIRE_FLAG is 0
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['ALBUMIN'].isnull())
data.loc[condition, 'ALBUMIN'] = median_albumin

# Calculate the median of ALBUMIN from data1
median_albumin = data1['ALBUMIN'].median()
print(f"Median ALBUMIN from data1: {median_albumin}")

# Replace missing ALBUMIN values in data where HOSPITAL_EXPIRE_FLAG is 1
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 1) & (data['ALBUMIN'].isnull())
data.loc[condition, 'ALBUMIN'] = median_albumin

Median ALBUMIN from data0: 3.15
Median ALBUMIN from data1: 2.7875


# Calculate the median of BILIRUBIN from data0
median_bilirubin = data0['BILIRUBIN'].median()
print(f"Median BILIRUBIN from data0: {median_bilirubin}")

# Replace missing BILIRUBIN values in data where HOSPITAL_EXPIRE_FLAG is 0
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['BILIRUBIN'].isnull())
data.loc[condition, 'BILIRUBIN'] = median_bilirubin

# Calculate the median of BILIRUBIN from data1
median_bilirubin = data1['BILIRUBIN'].median()
print(f"Median BILIRUBIN from data1: {median_bilirubin}")

# Replace missing BILIRUBIN values in data where HOSPITAL_EXPIRE_FLAG is 1
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 1) & (data['BILIRUBIN'].isnull())
data.loc[condition, 'BILIRUBIN'] = median_bilirubin

Median BILIRUBIN from data0: 0.6
Median BILIRUBIN from data1: 0.9


# Calculate the median of LACTATE from data0
median_lactate = data0['LACTATE'].median()
print(f"Median LACTATE from data0: {median_lactate}")

# Replace missing LACTATE values in data where HOSPITAL_EXPIRE_FLAG is 0
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['LACTATE'].isnull())
data.loc[condition, 'LACTATE'] = median_lactate

# Calculate the median of LACTATE from data1
median_lactate = data1['LACTATE'].median()
print(f"Median LACTATE from data1: {median_lactate}")

# Replace missing LACTATE values in data where HOSPITAL_EXPIRE_FLAG is 1
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 1) & (data['LACTATE'].isnull())
data.loc[condition, 'LACTATE'] = median_lactate

Median LACTATE from data0: 1.55
Median LACTATE from data1: 2.0


# Calculate the median of CREATININE from data0
median_creatinine = data0['CREATININE'].median()
print(f"Median CREATININE from data0: {median_creatinine}")

# Replace missing CREATININE values in data where HOSPITAL_EXPIRE_FLAG is 0
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['CREATININE'].isnull())
data.loc[condition, 'CREATININE'] = median_creatinine

# Calculate the median of CREATININE from data1
median_creatinine = data1['CREATININE'].median()
print(f"Median CREATININE from data1: {median_creatinine}")

# Replace missing CREATININE values in data where HOSPITAL_EXPIRE_FLAG is 1
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 1) & (data['CREATININE'].isnull())
data.loc[condition, 'CREATININE'] = median_creatinine

Median CREATININE from data0: 0.875
Median CREATININE from data1: 1.375


median_PLATELET_COUNT = data0['PLATELET_COUNT'].median()
print(f"Median PLATELET_COUNT from data0: {median_PLATELET_COUNT}")

condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['PLATELET_COUNT'].isnull())
data.loc[condition, 'PLATELET_COUNT'] = median_PLATELET_COUNT

Median PLATELET_COUNT from data0: 219.0


# Calculate the median of PTT from data0
median_ptt = data0['PTT'].median()
print(f"Median PTT from data0: {median_ptt}")

# Replace missing PTT values in data where HOSPITAL_EXPIRE_FLAG is 0
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 0) & (data['PTT'].isnull())
data.loc[condition, 'PTT'] = median_ptt

# Calculate the median of PTT from data1
median_ptt = data1['PTT'].median()
print(f"Median PTT from data1: {median_ptt}")

# Replace missing PTT values in data where HOSPITAL_EXPIRE_FLAG is 1
condition = (data['HOSPITAL_EXPIRE_FLAG'] == 1) & (data['PTT'].isnull())
data.loc[condition, 'PTT'] = median_ptt

Median PTT from data0: 31.6
Median PTT from data1: 38.75


### Making sure there is no more missing values

data.isnull().sum()

AGE                     0
GENDER                  0
ETHNICITY               0
HEART_RATE              0
TEMPERATURE             0
RESP_RATE               0
ALBUMIN                 0
BUN                     0
BILIRUBIN               0
LACTATE                 0
BICARBONATE             0
CHLORIDE                0
CREATININE              0
GLUCOSE                 0
HEMOGLOBIN              0
HEMATOCRIT              0
PLATELET_COUNT          0
POTASSIUM               0
PTT                     0
SODIUM                  0
WBC                     0
HOSPITAL_EXPIRE_FLAG    0
dtype: int64


cols = list(data.columns)
num_cols = ['AGE','HEART_RATE','TEMPERATURE', 'RESP_RATE', 'ALBUMIN', 'BUN', 'BILIRUBIN', 'LACTATE', 'BICARBONATE', 'CHLORIDE', 'CREATININE', 'GLUCOSE', 'HEMOGLOBIN', 'HEMATOCRIT', 'PLATELET_COUNT', 'POTASSIUM', 'PTT', 'SODIUM', 'WBC', 'HOSPITAL_EXPIRE_FLAG']


# Store the results
kl_divergence_results = []

# Function to calculate KL divergence
def kl_divergence(p, q):
    return entropy(p, q)

# Iterate over each numerical column
for col in num_cols:
    col_data = data[col]
    
    # Calculate the probability distributions
    hist, bin_edges = np.histogram(col_data.dropna(), bins=30, density=True)
    
    # Assume normal distribution as reference distribution
    reference_distribution = norm.pdf(bin_edges[:-1], np.mean(col_data.dropna()), np.std(col_data.dropna()))
    
    # Normalize the histogram to make it a valid probability distribution
    hist /= np.sum(hist)
    reference_distribution /= np.sum(reference_distribution)
    
    # Calculate KL divergence
    kl_div = kl_divergence(hist, reference_distribution)
    kl_divergence_results.append({'Feature': col, 'KL Divergence': kl_div})

# Convert results to DataFrame
kl_divergence_df = pd.DataFrame(kl_divergence_results)

# Display KL divergence results
print(kl_divergence_df)

                 Feature  KL Divergence
0                    AGE       0.065410
1             HEART_RATE       0.040935
2            TEMPERATURE       0.294249
3              RESP_RATE       0.256393
4                ALBUMIN       0.263427
5                    BUN       0.300652
6              BILIRUBIN       1.260128
7                LACTATE       0.474169
8            BICARBONATE       0.053181
9               CHLORIDE       0.035973
10            CREATININE       0.531361
11               GLUCOSE       0.225293
12            HEMOGLOBIN       0.073793
13            HEMATOCRIT       0.080001
14        PLATELET_COUNT       0.156951
15             POTASSIUM       0.060117
16                   PTT       0.373272
17                SODIUM       0.048403
18                   WBC       0.471390
19  HOSPITAL_EXPIRE_FLAG       2.927277


num_cols_no_target = ['AGE','HEART_RATE','TEMPERATURE', 'RESP_RATE', 'ALBUMIN', 'BUN', 'BILIRUBIN', 'LACTATE', 'BICARBONATE', 'CHLORIDE', 'CREATININE', 'GLUCOSE', 'HEMOGLOBIN', 'HEMATOCRIT', 'PLATELET_COUNT', 'POTASSIUM', 'PTT', 'SODIUM', 'WBC']


plt.figure(figsize=(13, 10))

sns.pairplot(data[num_cols], 
             diag_kind='hist', corner=True, diag_kws={'color': 'red'})

plt.yticks(rotation=0)
plt.show()

<Figure size 1300x1000 with 0 Axes>


plt.figure(figsize=(30, 30))

corr = data.corr() # correlation
mask = np.triu(np.ones_like(corr, dtype=bool)) # masking the upper triangle
np.fill_diagonal(mask, False) # diagonal 1s

# heatmap
sns.heatmap(corr, annot=True, cmap='coolwarm', mask=mask)

plt.yticks(rotation=0)
plt.show()

C:\Users\andre\AppData\Local\Temp\ipykernel_20324\1926582375.py:3: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.
  corr = data.corr() # correlation


df_with_const = add_constant(data[num_cols_no_target])

vif = pd.DataFrame()
vif["feature"] = df_with_const.columns
vif["VIF"] = [variance_inflation_factor(df_with_const.values, i) for i in range(df_with_const.shape[1])]
3
vif


from scipy.spatial.distance import mahalanobis
from scipy.stats import chi2
from sklearn.preprocessing import StandardScaler

# Calculate the mean and covariance matrix on the scaled data
mean = np.mean(data[num_cols], axis=0)
cov = np.cov(data[num_cols], rowvar=False)
inv_covmat = np.linalg.inv(cov)

# Calculate Mahalanobis distance for each observation
def mahalanobis_distance(row, mean, inv_covmat):
    diff = row - mean
    return np.sqrt(np.dot(np.dot(diff, inv_covmat), diff.T))

data['mahalanobis'] = pd.DataFrame(data[num_cols], columns=num_cols).apply(lambda row: mahalanobis_distance(row, mean, inv_covmat), axis=1)

# Determine the threshold for the 99% confidence interval
threshold = chi2.ppf(0.99, len(num_cols))

# Identify outliers (note: using np.sqrt(threshold) for the distance)
outliers = data[data['mahalanobis'] > np.sqrt(threshold)]

# Print the outliers DataFrame
print("Outliers:")
print(outliers)

Outliers:
        AGE GENDER               ETHNICITY  HEART_RATE  TEMPERATURE  \
11     55.0      F                 UNKNOWN   93.750000    97.522917   
29     89.0      F                   WHITE   80.166667    98.250000   
36     44.0      F                 UNKNOWN   87.750000    97.887500   
38     60.0      M                   WHITE   85.357143    96.562500   
66     53.0      F                   WHITE   74.500000    98.112500   
...     ...    ...                     ...         ...          ...   
22515  83.0      F  BLACK/AFRICAN AMERICAN   45.375000    95.912500   
22533  65.0      F                 UNKNOWN  126.609375    96.287500   
22545  60.0      M                   WHITE   86.016667    99.800000   
22555  66.0      F                 UNKNOWN  106.750000    98.100000   
22564  76.0      M                   WHITE  108.125000    99.387500   

       RESP_RATE   ALBUMIN        BUN  BILIRUBIN    LACTATE  BICARBONATE  \
11     23.750000  3.666667  58.375000  35.600000   2.700000    20.125000   
29     17.437500  3.350000  84.125000   0.500000   2.800000    30.875000   
36     16.125000  2.242857  11.187500  17.175000   3.256250    16.250000   
38     27.000000  2.200000  33.000000  14.212500  10.187500    10.812500   
66      9.000000  4.760000  84.937500  35.275000   4.033333    13.750000   
...          ...       ...        ...        ...        ...          ...   
22515  24.312500  1.700000  22.416667   1.412500   3.081250    16.270833   
22533  12.937500  2.350000  32.714286   1.900000   7.162500    11.187500   
22545  29.741667  3.000000  44.125000   1.128571   4.012500    16.750000   
22555  12.000000  3.400000  49.500000   4.637500   1.210417    20.750000   
22564  17.125000  1.850000  74.875000   0.866667   3.587500    13.875000   

         CHLORIDE  CREATININE     GLUCOSE  HEMOGLOBIN  HEMATOCRIT  \
11     107.375000    2.150000  176.125000    7.906250   23.691667   
29      90.625000    3.125000  259.500000    9.912500   32.575000   
36     107.875000    0.725000  167.062500    8.495833   25.897917   
38      98.125000    1.975000  174.062500    8.518750   24.018750   
66      87.250000    5.793750  118.937500    7.875000   23.462500   
...           ...         ...         ...         ...         ...   
22515  112.833333    1.283333  121.645833   11.300000   36.444444   
22533   98.375000    2.642857  211.875000    7.707143   25.578571   
22545  104.500000    3.737500  164.000000    9.100000   27.206250   
22555   91.625000    3.750000  115.750000    9.200000   26.381250   
22564  102.375000    2.525000  230.125000    9.475000   29.375000   

       PLATELET_COUNT  POTASSIUM       PTT      SODIUM        WBC  \
11          81.687500   3.875000  50.32500  142.500000  20.068750   
29         150.625000   3.650000  54.36250  136.500000   9.675000   
36          93.354167   3.743750  51.96250  139.937500  38.395833   
38          43.875000   4.550000  94.10625  131.937500   6.243750   
66          78.250000   3.856250  60.45000  127.375000   9.687500   
...               ...        ...       ...         ...        ...   
22515       88.555556   4.400000  57.80000  136.041667  12.194444   
22533      154.214286   4.143750  74.65000  138.000000  19.471429   
22545       70.083333   5.428571  78.68125  138.428571  16.812500   
22555      469.125000   4.237500  64.25000  133.625000  33.187500   
22564       83.000000   3.925000  35.55625  129.000000  25.975000   

       HOSPITAL_EXPIRE_FLAG  mahalanobis  
11                        1     9.852989  
29                        1     6.170727  
36                        1     6.919341  
38                        1     9.486908  
66                        1    11.231063  
...                     ...          ...  
22515                     1     7.057887  
22533                     1     8.731445  
22545                     1     6.201820  
22555                     1     6.876449  
22564                     1     6.807305  

[1993 rows x 23 columns]


data.to_csv('cleaned_health.csv', index=False)

	SUBJECT_ID	HADM_ID	ICUSTAY_ID	AGE	GENDER	ETHNICITY	HEART_RATE	DIASBP	SYSTBP	MABP	TEMPERATURE	O2SAT	RESP_RATE	ALBUMIN	BUN	BILIRUBIN	LACTATE	BICARBONATE	BAND_NEUTROPHIL	CHLORIDE	CREATININE	GLUCOSE	HEMOGLOBIN	HEMATOCRIT	PLATELET_COUNT	POTASSIUM	PTT	SODIUM	WBC	HOSPITAL_EXPIRE_FLAG
0	18868417	21481340	36475723	77	M	OTHER	74.250	NaN	NaN	NaN	98.1125	NaN	18.375	NaN	33.375000	NaN	1.300000	27.875	NaN	105.0000	1.537500	105.250000	15.47500	49.75000	169.0000	4.000	75.287500	141.875	9.5625	0
1	17030222	22455492	30262362	85	F	WHITE	77.625	24.125	40.875	NaN	97.3875	NaN	12.250	NaN	25.400000	NaN	1.483333	26.000	NaN	106.2000	0.740000	120.600000	12.27500	37.45000	311.2500	3.940	43.066667	142.600	9.1500	1
2	15664318	21206710	38572720	44	F	OTHER	103.750	120.250	130.250	NaN	98.5125	97.0	20.625	2.6	22.250000	0.25	1.610000	26.500	NaN	102.6250	3.937500	98.250000	7.73750	26.21250	496.7500	4.575	32.000000	139.500	17.9750	0
3	13970700	20870207	38790488	91	F	WHITE	69.625	52.625	133.500	NaN	97.3625	NaN	17.750	NaN	16.833333	NaN	NaN	25.000	NaN	101.5625	0.641667	94.083333	11.03125	30.93125	212.8125	3.875	36.700000	133.500	7.7125	0
4	17035582	20664949	37164270	63	M	WHITE	81.625	42.875	97.000	NaN	98.2750	NaN	25.625	NaN	29.500000	0.50	2.450000	23.625	NaN	105.3750	0.900000	129.250000	11.18750	30.02500	218.9375	4.325	31.171429	140.125	11.3000	0

	SUBJECT_ID	HADM_ID	ICUSTAY_ID	AGE	GENDER	ETHNICITY	HEART_RATE	DIASBP	SYSTBP	MABP	TEMPERATURE	O2SAT	RESP_RATE	ALBUMIN	BUN	BILIRUBIN	LACTATE	BICARBONATE	BAND_NEUTROPHIL	CHLORIDE	CREATININE	GLUCOSE	HEMOGLOBIN	HEMATOCRIT	PLATELET_COUNT	POTASSIUM	PTT	SODIUM	WBC
0	18868417	21481340	36475723	77	M	OTHER	74.250	NaN	NaN	NaN	98.1125	NaN	18.375	NaN	33.375000	NaN	1.30	27.875	NaN	105.0000	1.537500	105.250000	15.47500	49.75000	169.0000	4.0000	75.287500	141.875	9.5625
2	15664318	21206710	38572720	44	F	OTHER	103.750	120.250	130.25	NaN	98.5125	97.0	20.625	2.600000	22.250000	0.250	1.61	26.500	NaN	102.6250	3.937500	98.250000	7.73750	26.21250	496.7500	4.5750	32.000000	139.500	17.9750
3	13970700	20870207	38790488	91	F	WHITE	69.625	52.625	133.50	NaN	97.3625	NaN	17.750	NaN	16.833333	NaN	NaN	25.000	NaN	101.5625	0.641667	94.083333	11.03125	30.93125	212.8125	3.8750	36.700000	133.500	7.7125
4	17035582	20664949	37164270	63	M	WHITE	81.625	42.875	97.00	NaN	98.2750	NaN	25.625	NaN	29.500000	0.500	2.45	23.625	NaN	105.3750	0.900000	129.250000	11.18750	30.02500	218.9375	4.3250	31.171429	140.125	11.3000
5	10457824	25280974	32230380	80	M	UNKNOWN	109.500	NaN	NaN	NaN	98.2875	NaN	28.375	2.166667	7.000000	0.925	1.20	28.125	6.2	99.2500	0.550000	164.375000	8.18750	24.77500	588.0000	4.0125	63.393750	138.750	19.0250

	SUBJECT_ID	HADM_ID	ICUSTAY_ID	AGE	GENDER	ETHNICITY	HEART_RATE	DIASBP	SYSTBP	MABP	TEMPERATURE	O2SAT	RESP_RATE	ALBUMIN	BUN	BILIRUBIN	LACTATE	BICARBONATE	BAND_NEUTROPHIL	CHLORIDE	CREATININE	GLUCOSE	HEMOGLOBIN	HEMATOCRIT	PLATELET_COUNT	POTASSIUM	PTT	SODIUM	WBC	HOSPITAL_EXPIRE_FLAG
1	17030222	22455492	30262362	85	F	WHITE	77.625000	24.125000	40.875000	NaN	97.387500	NaN	12.2500	NaN	25.400000	NaN	1.483333	26.000000	NaN	106.200000	0.740000	120.600000	12.27500	37.450000	311.250000	3.940000	43.066667	142.600000	9.15000	1
11	14405232	24340879	31011196	55	F	UNKNOWN	93.750000	NaN	NaN	NaN	97.522917	NaN	23.7500	3.666667	58.375000	35.6000	2.700000	20.125000	0.000	107.375000	2.150000	176.125000	7.90625	23.691667	81.687500	3.875000	50.325000	142.500000	20.06875	1
15	10641937	22804676	33298911	63	M	WHITE	99.979167	50.833333	72.666667	NaN	99.025000	NaN	22.8750	2.712500	91.250000	8.4625	2.248958	16.500000	0.875	108.875000	2.362500	124.250000	7.76250	22.987500	23.187500	4.650000	43.787500	139.250000	3.99375	1
26	12026338	28548230	32163537	68	F	WHITE	89.750000	62.000000	96.250000	NaN	99.775000	99.0	17.1250	2.600000	20.333333	0.4000	2.585000	16.604167	NaN	107.958333	1.552083	118.104167	10.34375	31.327083	95.770833	4.966667	43.018750	137.541667	4.41875	1
29	11439927	23639754	37817300	89	F	WHITE	80.166667	19.000000	34.500000	NaN	98.250000	74.0	17.4375	3.350000	84.125000	0.5000	2.800000	30.875000	3.000	90.625000	3.125000	259.500000	9.91250	32.575000	150.625000	3.650000	54.362500	136.500000	9.67500	1

	Data_Type	No_Total_Value	No_Total_Missing_Value	Proportion_Missing_Value	Unique_Value	Total_Unique_Value
Variable
SUBJECT_ID	int64	22565	0	0.000	[18868417, 17030222, 15664318, 13970700, 17035...	22565
HADM_ID	int64	22565	0	0.000	[21481340, 22455492, 21206710, 20870207, 20664...	22565
ICUSTAY_ID	int64	22565	0	0.000	[36475723, 30262362, 38572720, 38790488, 37164...	22565
AGE	int64	22565	0	0.000	[77, 85, 44, 91, 63, 80, 60, 72, 68, 33, 74, 5...	73
GENDER	object	22565	0	0.000	[M, F]	2
ETHNICITY	object	22565	0	0.000	[OTHER, WHITE, UNKNOWN, BLACK/AFRICAN AMERICAN...	8
HEART_RATE	float64	22565	1	0.000	[74.25, 77.625, 103.75, 69.625, 81.625, 109.5,...	2298
DIASBP	float64	22565	10265	0.455	[nan, 24.125, 120.25, 52.625, 42.875, 79.125, ...	1870
SYSTBP	float64	22565	10272	0.455	[nan, 40.875, 130.25, 133.5, 97.0, 163.34375, ...	2297
MABP	float64	22565	19878	0.881	[nan, 99.375, 71.625, 68.0, 78.1875, 68.166666...	1137
TEMPERATURE	float64	22565	94	0.004	[98.1125, 97.3875, 98.5125, 97.3625, 98.275, 9...	1240
O2SAT	float64	22565	13816	0.612	[nan, 97.0, 98.5, 96.5, 89.8, 96.375, 93.0, 99...	383
RESP_RATE	float64	22565	1	0.000	[18.375, 12.25, 20.625, 17.75, 25.625, 28.375,...	1345
ALBUMIN	float64	22565	7511	0.333	[nan, 2.6, 2.166666667, 3.308333333, 4.1, 3.6,...	692
BUN	float64	22565	0	0.000	[33.375, 25.4, 22.25, 16.833333333, 29.5, 7.0,...	2522
BILIRUBIN	float64	22565	5788	0.257	[nan, 0.25, 0.5, 0.925, 0.7375, 0.52, 0.7, 35....	1800
LACTATE	float64	22565	3918	0.174	[1.3, 1.483333333, 1.61, nan, 2.45, 1.2, 1.928...	3005
BICARBONATE	float64	22565	0	0.000	[27.875, 26.0, 26.5, 25.0, 23.625, 28.125, 26....	1071
BAND_NEUTROPHIL	float64	22565	16661	0.738	[nan, 6.2, 0.0, 0.875, 0.5, 3.0, 6.4, 8.125, 6...	344
CHLORIDE	float64	22565	0	0.000	[105.0, 106.2, 102.625, 101.5625, 105.375, 99....	1263
CREATININE	float64	22565	4	0.000	[1.5375, 0.74, 3.9375, 0.6416666667, 0.9, 0.55...	1698
GLUCOSE	float64	22565	0	0.000	[105.25, 120.6, 98.25, 94.083333333, 129.25, 1...	3975
HEMOGLOBIN	float64	22565	0	0.000	[15.475, 12.275, 7.7375, 11.03125, 11.1875, 8....	2844
HEMATOCRIT	float64	22565	0	0.000	[49.75, 37.45, 26.2125, 30.93125, 30.025, 24.7...	5366
PLATELET_COUNT	float64	22565	1	0.000	[169.0, 311.25, 496.75, 212.8125, 218.9375, 58...	8797
POTASSIUM	float64	22565	0	0.000	[4.0, 3.94, 4.575, 3.875, 4.325, 4.0125, 4.125...	1036
PTT	float64	22565	652	0.029	[75.2875, 43.066666667, 32.0, 36.7, 31.1714285...	8318
SODIUM	float64	22565	0	0.000	[141.875, 142.6, 139.5, 133.5, 140.125, 138.75...	1098
WBC	float64	22565	0	0.000	[9.5625, 9.15, 17.975, 7.7125, 11.3, 19.025, 1...	5288
HOSPITAL_EXPIRE_FLAG	int64	22565	0	0.000	[0, 1]	2

	Data_Type	No_Total_Value	No_Total_Missing_Value	Proportion_Missing_Value	Unique_Value	Total_Unique_Value
Variable
SUBJECT_ID	int64	19286	0	0.000	[18868417, 15664318, 13970700, 17035582, 10457...	19286
HADM_ID	int64	19286	0	0.000	[21481340, 21206710, 20870207, 20664949, 25280...	19286
ICUSTAY_ID	int64	19286	0	0.000	[36475723, 38572720, 38790488, 37164270, 32230...	19286
AGE	int64	19286	0	0.000	[77, 44, 91, 63, 80, 60, 72, 68, 33, 74, 65, 4...	73
GENDER	object	19286	0	0.000	[M, F]	2
ETHNICITY	object	19286	0	0.000	[OTHER, WHITE, UNKNOWN, BLACK/AFRICAN AMERICAN...	8
HEART_RATE	float64	19286	1	0.000	[74.25, 103.75, 69.625, 81.625, 109.5, 104.125...	1627
DIASBP	float64	19286	8997	0.467	[nan, 120.25, 52.625, 42.875, 79.125, 50.25, 7...	1488
SYSTBP	float64	19286	9003	0.467	[nan, 130.25, 133.5, 97.0, 163.34375, 123.75, ...	1762
MABP	float64	19286	17243	0.894	[nan, 99.375, 71.625, 68.0, 78.1875, 68.166666...	917
TEMPERATURE	float64	19286	32	0.002	[98.1125, 98.5125, 97.3625, 98.275, 98.2875, 9...	1027
O2SAT	float64	19286	12231	0.634	[nan, 97.0, 98.5, 96.5, 89.8, 96.375, 93.0, 90...	314
RESP_RATE	float64	19286	1	0.000	[18.375, 20.625, 17.75, 25.625, 28.375, 18.187...	887
ALBUMIN	float64	19286	6898	0.358	[nan, 2.6, 2.166666667, 3.308333333, 4.1, 3.6,...	611
BUN	float64	19286	0	0.000	[33.375, 22.25, 16.833333333, 29.5, 7.0, 25.25...	2043
BILIRUBIN	float64	19286	5439	0.282	[nan, 0.25, 0.5, 0.925, 0.7375, 0.52, 0.7, 0.4...	1240
LACTATE	float64	19286	3748	0.194	[1.3, 1.61, nan, 2.45, 1.2, 1.928125, 1.3375, ...	2306
BICARBONATE	float64	19286	0	0.000	[27.875, 26.5, 25.0, 23.625, 28.125, 26.25, 29...	854
BAND_NEUTROPHIL	float64	19286	14944	0.775	[nan, 6.2, 0.0, 0.5, 3.0, 5.125, 21.0, 9.4, 1....	286
CHLORIDE	float64	19286	0	0.000	[105.0, 102.625, 101.5625, 105.375, 99.25, 103...	1046
CREATININE	float64	19286	1	0.000	[1.5375, 3.9375, 0.6416666667, 0.9, 0.55, 0.96...	1400
GLUCOSE	float64	19286	0	0.000	[105.25, 98.25, 94.083333333, 129.25, 164.375,...	3395
HEMOGLOBIN	float64	19286	0	0.000	[15.475, 7.7375, 11.03125, 11.1875, 8.1875, 9....	2625
HEMATOCRIT	float64	19286	0	0.000	[49.75, 26.2125, 30.93125, 30.025, 24.775, 28....	4886
PLATELET_COUNT	float64	19286	1	0.000	[169.0, 496.75, 212.8125, 218.9375, 588.0, 120...	7879
POTASSIUM	float64	19286	0	0.000	[4.0, 4.575, 3.875, 4.325, 4.0125, 4.125, 3.76...	864
PTT	float64	19286	612	0.032	[75.2875, 32.0, 36.7, 31.171428571, 63.39375, ...	7219
SODIUM	float64	19286	0	0.000	[141.875, 139.5, 133.5, 140.125, 138.75, 139.8...	892
WBC	float64	19286	0	0.000	[9.5625, 17.975, 7.7125, 11.3, 19.025, 13.9625...	4423
HOSPITAL_EXPIRE_FLAG	int64	19286	0	0.000	[0]	1

Background information¶

Aggregating the Time-Series Data¶

References:¶

Exploratory Data Analysis¶

Checking for missing values¶

Dropping unused columns¶

Target Feature¶

Categorical Features¶

Numerical Features¶

Checking for Valid Range¶

Checking for distribution of each numerical features¶

Handling Missing Values¶

HEART_RATE¶

DIASBP and SYSTBP¶

MABP and O2SAT¶

BAND_NEUTROPHIL¶

TEMPERATURE¶

RESP_RATE¶

ALBUMIN¶

BILIRUBIN¶

LACTATE¶

CREATININE¶

PLATELET_COUNT¶

PTT¶

Rechecking KL Divergence¶

Bivariate Analysis¶

Identifying multidimensional outliers using Mahalanobis distance¶

Converting cleaned data to csv¶

	Feature	Description	MIN	MAX	UNIT
0	AGE	The age of the patient.	0.0	91	years
1	HEART_RATE	Heart Rate: The average heart rate of the pati...	0.0	350	bpm
2	DIASBP	Diastolic Blood Pressure (diasbp): The average...	0.0	375	mmHg
3	SYSTBP	Systolic Blood Pressure (systbp): The average ...	0.0	375	mmHg
4	MABP	Mean Blood Pressure (meanbp): The average mean...	14.0	330	mmHg
5	TEMPERATURE	Temperature: The average body temperature of t...	78.8	113	°F
6	O2SAT	Oxygen Saturation (o2sat): The average oxygen ...	0.0	100	%
7	RESP_RATE	Respiratory Rate (resp_rate): The average resp...	0.0	300	breaths per minute
8	ALBUMIN	Albumin: The average albumin level in the blood.	0.6	6	g/dL
9	BUN	Blood Urea Nitrogen (bun): The average blood u...	0.0	250	mg/dL
10	BILIRUBIN	Bilirubin: The average bilirubin level.	0.1	60	mg/dL
11	LACTATE	Lactate: The average lactate level in the blood.	0.4	30	mmol/L
12	BICARBONATE	Bicarbonate: The average bicarbonate level.	0.0	60	mEq/L
13	CHLORIDE	Chloride: The average chloride level.	50.0	175	mEq/L
14	CREATININE	Creatinine: The average creatinine level.	0.1	60	mg/dL
15	GLUCOSE	Glucose: The average glucose level.	33.0	2000	mg/dL
16	HEMOGLOBIN	Hemoglobin: The average hemoglobin level.	0.0	25	g/dL
17	HEMATOCRIT	Hematocrit: The average hematocrit level.	0.0	75	g/dL
18	PLATELET_COUNT	Platelet Count: The average platelet count.	0.0	2000	1000/mm³
19	POTASSIUM	Potassium: The average potassium level.	0.0	12	mEq/L
20	PTT	Partial Thromboplastin Time (PTT): The average...	18.8	150	seconds
21	SODIUM	Sodium: The average sodium level.	50.0	225	mEq/L
22	WBC	White Blood Cells: The average white blood cel...	0.0	1000	1000/mm³
23	BAND_NEUTROPHIL	Band Neutrophil: The percentage of band neutro...	0.0	100	%

	Feature	Missing Values	Below MIN	Above MAX	Total Valid Values
0	AGE	0	0	0	22565
1	HEART_RATE	1	0	0	22564
2	DIASBP	10265	1	7	12292
3	SYSTBP	10272	0	0	12293
4	MABP	19878	36	4	2647
5	TEMPERATURE	94	10	8	22453
6	O2SAT	13816	0	11	8738
7	RESP_RATE	1	0	1	22563
8	ALBUMIN	7511	0	0	15054
9	BUN	0	0	0	22565
10	BILIRUBIN	5788	3	2	16772
11	LACTATE	3918	3	1	18643
12	BICARBONATE	0	0	0	22565
13	CHLORIDE	0	0	0	22565
14	CREATININE	4	2	0	22559
15	GLUCOSE	0	0	0	22565
16	HEMOGLOBIN	0	0	0	22565
17	HEMATOCRIT	0	0	0	22565
18	PLATELET_COUNT	1	0	0	22564
19	POTASSIUM	0	0	0	22565
20	PTT	652	3	0	21910
21	SODIUM	0	0	0	22565
22	WBC	0	0	0	22565
23	BAND_NEUTROPHIL	16661	0	0	5904

	Feature	Missing Values	Below MIN	Above MAX	Total Valid Values
0	AGE	0	0	0	19286
1	HEART_RATE	1	0	0	19285
2	DIASBP	8997	1	4	10284
3	SYSTBP	9003	0	0	10283
4	MABP	17243	28	3	2012
5	TEMPERATURE	32	3	8	19243
6	O2SAT	12231	0	8	7047
7	RESP_RATE	1	0	1	19284
8	ALBUMIN	6898	0	0	12388
9	BUN	0	0	0	19286
10	BILIRUBIN	5439	3	0	13844
11	LACTATE	3748	2	1	15535
12	BICARBONATE	0	0	0	19286
13	CHLORIDE	0	0	0	19286
14	CREATININE	1	2	0	19283
15	GLUCOSE	0	0	0	19286
16	HEMOGLOBIN	0	0	0	19286
17	HEMATOCRIT	0	0	0	19286
18	PLATELET_COUNT	1	0	0	19285
19	POTASSIUM	0	0	0	19286
20	PTT	612	2	0	18672
21	SODIUM	0	0	0	19286
22	WBC	0	0	0	19286
23	BAND_NEUTROPHIL	14944	0	0	4342

	Feature	Missing Values	Below MIN	Above MAX	Total Valid Values
0	AGE	0	0	0	3279
1	HEART_RATE	0	0	0	3279
2	DIASBP	1268	0	3	2008
3	SYSTBP	1269	0	0	2010
4	MABP	2635	8	1	635
5	TEMPERATURE	62	7	0	3210
6	O2SAT	1585	0	3	1691
7	RESP_RATE	0	0	0	3279
8	ALBUMIN	613	0	0	2666
9	BUN	0	0	0	3279
10	BILIRUBIN	349	0	2	2928
11	LACTATE	170	1	0	3108
12	BICARBONATE	0	0	0	3279
13	CHLORIDE	0	0	0	3279
14	CREATININE	3	0	0	3276
15	GLUCOSE	0	0	0	3279
16	HEMOGLOBIN	0	0	0	3279
17	HEMATOCRIT	0	0	0	3279
18	PLATELET_COUNT	0	0	0	3279
19	POTASSIUM	0	0	0	3279
20	PTT	40	1	0	3238
21	SODIUM	0	0	0	3279
22	WBC	0	0	0	3279
23	BAND_NEUTROPHIL	1717	0	0	1562

	feature	VIF
0	const	14685.458965
1	AGE	1.207572
2	HEART_RATE	1.166075
3	TEMPERATURE	1.096312
4	RESP_RATE	1.106975
5	ALBUMIN	1.208824
6	BUN	2.131926
7	BILIRUBIN	1.209277
8	LACTATE	1.294945
9	BICARBONATE	2.748871
10	CHLORIDE	5.180620
11	CREATININE	1.900004
12	GLUCOSE	1.098345
13	HEMOGLOBIN	16.071140
14	HEMATOCRIT	15.795112
15	PLATELET_COUNT	1.239323
16	POTASSIUM	1.215595
17	PTT	1.082323
18	SODIUM	4.122088
19	WBC	1.110443

	Data_Type	No_Total_Value	No_Total_Missing_Value	Proportion_Missing_Value	Unique_Value	Total_Unique_Value
Variable
SUBJECT_ID	int64	3279	0	0.000	[17030222, 14405232, 10641937, 12026338, 11439...	3279
HADM_ID	int64	3279	0	0.000	[22455492, 24340879, 22804676, 28548230, 23639...	3279
ICUSTAY_ID	int64	3279	0	0.000	[30262362, 31011196, 33298911, 32163537, 37817...	3279
AGE	int64	3279	0	0.000	[85, 55, 63, 68, 89, 67, 44, 60, 66, 81, 58, 5...	73
GENDER	object	3279	0	0.000	[F, M]	2
ETHNICITY	object	3279	0	0.000	[WHITE, UNKNOWN, UNABLE TO OBTAIN, ASIAN, BLAC...	8
HEART_RATE	float64	3279	0	0.000	[77.625, 93.75, 99.979166667, 89.75, 80.166666...	1406
DIASBP	float64	3279	1268	0.387	[24.125, nan, 50.833333333, 62.0, 19.0, 56.653...	874
SYSTBP	float64	3279	1269	0.387	[40.875, nan, 72.666666667, 96.25, 34.5, 82.57...	1164
MABP	float64	3279	2635	0.804	[nan, 75.0, 79.625, 340.0, 82.8125, 102.0, 79....	468
TEMPERATURE	float64	3279	62	0.019	[97.3875, 97.522916667, 99.025, 99.775, 98.25,...	706
O2SAT	float64	3279	1585	0.483	[nan, 99.0, 74.0, 95.0, 97.75, 97.333333333, 9...	259
RESP_RATE	float64	3279	0	0.000	[12.25, 23.75, 22.875, 17.125, 17.4375, 24.843...	857
ALBUMIN	float64	3279	613	0.187	[nan, 3.666666667, 2.7125, 2.6, 3.35, 2.3, 2.2...	455
BUN	float64	3279	0	0.000	[25.4, 58.375, 91.25, 20.333333333, 84.125, 67...	1535
BILIRUBIN	float64	3279	349	0.106	[nan, 35.6, 8.4625, 0.4, 0.5, 2.433333333, 17....	1081
LACTATE	float64	3279	170	0.052	[1.483333333, 2.7, 2.248958333, 2.585, 2.8, 2....	1461
BICARBONATE	float64	3279	0	0.000	[26.0, 20.125, 16.5, 16.604166667, 30.875, 22....	735
BAND_NEUTROPHIL	float64	3279	1717	0.524	[nan, 0.0, 0.875, 3.0, 6.4, 8.125, 6.0, 8.0, 1...	231
CHLORIDE	float64	3279	0	0.000	[106.2, 107.375, 108.875, 107.958333333, 90.62...	871
CREATININE	float64	3279	3	0.001	[0.74, 2.15, 2.3625, 1.552083333, 3.125, 1.616...	1049
GLUCOSE	float64	3279	0	0.000	[120.6, 176.125, 124.25, 118.104166667, 259.5,...	1895
HEMOGLOBIN	float64	3279	0	0.000	[12.275, 7.90625, 7.7625, 10.34375, 9.9125, 9....	1285
HEMATOCRIT	float64	3279	0	0.000	[37.45, 23.691666667, 22.9875, 31.327083333, 3...	1998
PLATELET_COUNT	float64	3279	0	0.000	[311.25, 81.6875, 23.1875, 95.770833333, 150.6...	2599
POTASSIUM	float64	3279	0	0.000	[3.94, 3.875, 4.65, 4.966666667, 3.65, 4.40833...	695
PTT	float64	3279	40	0.012	[43.066666667, 50.325, 43.7875, 43.01875, 54.3...	2569
SODIUM	float64	3279	0	0.000	[142.6, 142.5, 139.25, 137.541666667, 136.5, 1...	788
WBC	float64	3279	0	0.000	[9.15, 20.06875, 3.99375, 4.41875, 9.675, 12.8...	2306
HOSPITAL_EXPIRE_FLAG	int64	3279	0	0.000	[1]	1